Chapter 9.2, Problem 70SR

To determine

Write an equation in point − slope form for the line passes through the point $(x_1,y_1)=(-1,-2)$ with a slope $m=-\frac{1}{2}$ .

Answer to Problem 70SR

The equation is: $y+2=-\frac{1}{2}x-\frac{1}{2}$

Explanation of Solution

Given:

Write an equation in point − slope form for the line passes through the point $(x_1,y_1)=(-1,-2)$ with a slope $m=-\frac{1}{2}$ .

Concept Used:

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

Calculation:

Point − slope form of equation: $y-y_1=m(x-x_1)$

Given: $(x_1,y_1)=(-1,-2),m=-\frac{1}{2}$

  $\begin{array}{l}y-y_1=m(x-x_1)\\ y-(-2)=-\frac{1}{2}(x--1)\\ y+2=-\frac{1}{2}(x+1)\\ y+2=-\frac{1}{2}x-\frac{1}{2}\end{array}$

Thus, the equation is: $y+2=-\frac{1}{2}x-\frac{1}{2}$